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Abstract—Applications such as undersea power prefer constant current dc distribution in a series trunk cable connection over dc voltage distribution in order to ...
Control of Series Connected Resonant Converter Modules in Constant Current DC Distribution Power Systems Hongjie Wang, Tarak Saha, and Regan Zane ECE Department Utah State University Logan, UT – USA 84341 e-mail: [email protected] Abstract—Applications such as undersea power prefer constant current dc distribution in a series trunk cable connection over dc voltage distribution in order to provide robustness against cable impedance and faults. Power converter modules employed in these architectures are connected in series and have a constant current input. In this paper, steady state analysis and a control strategy are presented for series connected resonant converter modules in a constant current dc distributed power system. The control strategy is developed to achieve stable operation of the system with no communications required among modules. Hardware results are provided for a system consisting of two series connected 100 kHz 500 W SRCs with 1 A trunk current and regulated output current. Keywords—dc DPS; resonant converter; series connected; constant current; multiple modules

I.

trunk cable and provides power to the load such as sensors. The DC/DC converter employed in this work is a series resonant converter (SRC) for its high efficiency. One of the findings in this work is that the steady state solutions and design considerations for SRCs with constant current input and constant voltage input differ significantly. This paper proposes design constraints and a control strategy for series connected SRC modules in the constant current dc DPS to achieve stable operation of the system and regulation of each SRC output current or voltage in the chain, which can be applied in both terrestrial and undersea constant current dc DPS. In this paper, the steady state analysis and design constraints for the SRC with constant current input are presented in Section II. In Section III, the system control strategy and stability analysis for series connected SRC

INTRODUCTION

The dc distributed power system (DPS) is widely employed in both terrestrial and undersea applications such as data centers, communication systems, renewable energy systems and undersea observatories, thanks to its high efficiency and high power density delivery capability [1-11]. Most of the research in the literature has focused on constant voltage dc DPS [1-9]. For a constant voltage architecture, the modules are parallel connected on a dc voltage bus. However, for some applications, such as underwater telecommunication and undersea observation system, a constant current dc power distribution from the shore is preferred over dc voltage to provide robustness against cable impedance and faults. In conventional underwater telecommunication systems, the constant current flows through a single trunk cable, and the return current flows through sea water [10]. In the Japanese ARENA project, supplying constant current to a mesh-like undersea cable-network for an undersea observation system is presented using current to current converters without control [11]. In both cases, the observation nodes are injected into the trunk cable, as illustrated in Fig. 1. In Fig. 1, trunk cables generally have a length of tens of kilometers or even longer, and each DC/DC converter represents an observation node which draws the power from The work presented in this paper was sponsored by the Raytheon Company through the Utah State University Power Electronics Lab (UPEL).

978-1-5090-1815-4/16/$31.00 ©2016 IEEE

ground connection

shore based dc current source

constant current trunk cable

Land Ocean

current to current SRC #1 constant current

trunk cable current to current SRC #2

constant current

constant current

to load

to load

trunk cable current to current SRC #n

to load

trunk cable seawater connection

Fig. 1. Architecture of a single cable undersea constant current dc DPS.

modules with constant current input are discussed. Hardware results are provided in Section IV to validate the proposed control strategy for a system consisting of two 100 kHz 500 W SRCs connected in a series chain fed by 1 A shore current, and the conclusions are given in Section V.

Q1

By using the sinusoidal approximation [12], the equivalent circuit can be derived as illustrated in Fig. 3 [13]. For the input bridge, the average approximation is applied to the input, while sinusoidal approximation is applied to the output. The input side is modeled as a dependent current source as the average value of input current is related to the resonant current. The output side is a dependent voltage source as the magnitude of the fundamental component is related to the input voltage. For the half-bridge voltage doubler, the scenario is similar. Sinusoidal approximation is applied to the input, while the average approximation is applied to the output. The input side is modeled as an equivalent resistor as the input voltage is in phase with the input current. The output side is a controlled current source as the average value of the output current is related to the resonant current. For the resonant inductor and capacitor, they are directly presented in the equivalent circuit as they are linear components. In Fig. 3, the equivalent resistance Re, the input current Iin and controlled voltage source vs1 are expressed as

Cin

I in =

vs1 =

2

π2

Rload ,

2 I s1

α

4

α

sin( )cos(ϕ s ) , π 2

V sin( )sin(ωs t ). π in 2

(1)

(2)

In Fig. 3, reflecting the equivalent resistance Re to the transformer primary side, the fundamental component of the resonant current is1 can be calculated as

Cout

vDC(t)

Q4

Rload

C

1:n

C2

D2

Fig. 2. SRC with constant input current topology.

is1

Iin +

Ig

Cin

Lr

Cr

' 1:n is1

I out

+

Re

Vin

_

Cout

v s1

1

π



Vout

Rload

I s' 1



Fig. 3. Equivalent circuit of the SRC topology.

Q1

t Q3

t

α Fig. 4. Definition of phase shift angle α.

1 4 α Vin sin sin(ωs t − ϕ s ) = I s1 sin(ωs t − ϕ s ) , (4) 2 Aπ

where

A= (

2 1 2 ) , Rload ) 2 + (ωs Lr − n 2π 2 ω s Cr

ωs Lr −

(3)

In (2) and (3), ϕs is the phase shift of resonant current is1 with respect to vs1, Is1 is the peak value of resonant current is1, and α is the phase shift angle of the input full bridge, which ranges from 0° to 180°. The definition of the phase shift angle α is illustrated in Fig. 4.

D

+

vAB(t) B Q2

is1 = Re =

+

A

C1

D1

Cr

Lr Ig

II. STEADY STATE ANALYSIS OF SRC WITH CONSTANT CURRENT INPUT Figure 2 illustrates the SRC topology analyzed in this paper. The input side is an active bridge consisting of devices Q1…Q4, while the output is a half-bridge voltage doubler consisting of diodes D1 and D2. The resonant tank consists of inductor Lr and capacitor Cr. A 1: n power transformer provides isolation between the input and output. The input is modeled as a constant current source as illustrated in Fig. 2. Phase-shift modulation is employed as the driving scheme.

Q3

ϕ s = arctan(

2 n 2π 2

I s1 =

(5)

1

ω s Cr

),

(6)

Rload

1 4 α Vin sin . 2 Aπ

(7)

As illustrated in Fig. 3, is1 is the transformer primary current. Based on the transformer turns ratio, the transformer secondary current equals

i ' s1 =

where

Vout =

1 4 α Vin sin sin(ωs t − ϕ s ) = I 's1 sin(ωs t − ϕ s ) ,(8) 2 A nπ

I ' s1 =

1 4 α Vin sin . 2 A nπ

(9)

From (9) and the relation between the output current and

I 's1 , the output current can be derived as 1 4 α V sin . 2 in 2 A nπ

I out =

(10)

For a resistive load, the output voltage and output power can be expressed as

1 4 α V sin Rload , 2 in 2 A nπ

(11)

1 4 α V sin ) 2 Rload . 2 in 2 A nπ

(12)

Vout = I out Rload =

Pout = Vout I out = (

For the input side of the SRC, Pin = Vin I g . Considering ideal case at here, the input power of the SRC should be equal to the output power, which can be described as

Pin = Vin I g = Pout = (

1 4 α V sin ) 2 Rload . 2 in 2 A nπ

Vin =

2

.

α

α

4sin( ) Rload 2

,

(16)

n 2π 4 A2 I g2

α

.

16sin 2 ( ) Rload 2

(17)

III. CONTROL STRATEGY A. Stability Analysis of a Constant Current Cascaded System Stability is a major concern in dc DPS because the system may become unstable even though the subsystems are stable in standalone mode. Many efforts have been made to define impedance specifications for a stable dc DPS [5-7]. However, in [5-7], authors focused on the constant voltage dc DPS, and based on the assumption that the output impedance of the source is known. Figure 5 shows two subsystems connected in series by a constant current chain. Gsource is the input-to-output transfer function of the source subsystem, while Gload is the input-tooutput transfer function of the load subsystem. The overall input-to-output transfer function can be expressed as

Goverall =

I out I out I in I s = Vs I in I s Vs

= Gload

(14)

Z o  Z in Zo Gsource = GsourceGload (18) Z in Z in + Z o

= GsourceGload

Substituting (14) into (10), (11) and (12), expression of the output current, output voltage and output power of an SRC with constant input current can be derived as

nπ 2 AI g

,

From the steady state solution shown in (14)-(17), it can be seen that the behavior of SRC with constant current input is different from the constant voltage input case: 1) Maximum phase shift (180°) results in minimum output power, while lower phase shift leads to an higher output power. 2) The SRC has a non-zero minimum output power, and phase shift modulation can’t be employed to obtain a zero output power. Hence, the SRC must be designed properly to guarantee that the minimum output current is lower than the objective for the entire load range.

16sin ( ) Rload 2

I out =

α

4sin( ) 2

(13)

From (13), the SRC input voltage can be expressed as

n 2π 4 A2 I g

Pout =

nπ 2 AI g

(15)

with

1 , 1 + Tm Tm = Z in Z o .

(19)

Source subsystem

+ Vs -

Is

Iin

Gsource

Load subsystem

Ig

Iout

Gload

SRC Controller

SRC gate signals

Zin

Fig. 5. Two constant current cascaded system.

In (18) and (19), Zo is the output impedance of the source subsystem, and Zin is the input impedance of the load subsystem. Similar to the minor loop gain defined in a voltage cascaded system [14], the minor loop gain for a constant current cascaded system can be defined as Tm = Zin / Zo, which can be employed to determine the stability of a constant current dc DPS. If multiple load subsystems are distributed along the constant current trunk, the overall Zin will be the sum of each load subsystem’s input impedance plus the impedance of the entire trunk cable, since they are connected in series. If |Zo|>>|Zin| for all frequencies, the whole constant current dc DPS is stable, assuming that the load subsystems are individually stable. B. Control Stragety If the output impedance of the source is known, the impedance specifications presented in [5-7] can be used to develop a control strategy that guarantees the stable operation of the dc DPS. However, in some practical applications, the output impedance of the source may not be available a priori. In these cases, the impedance specifications mentioned in the literatures become difficult to implement. For the undersea constant current dc DPS investigated in this work, the shore based current source is a commercial product without an output impedance description, while the controller bandwidth is known. For an output current or output voltage regulated converter, the closed loop input impedance is a negative resistance over a frequency range lower than the crossover frequency, while it is the open loop input impedance over the frequency range higher than the crossover frequency. If the shore based current source has a crossover frequency higher than the load SRC module, the load impedance seen by the source at higher frequencies is the open loop input impedance of the SRC module. In this case, the high output impedance of the constant current source covers the stability condition up to its crossover frequency, and overall stability is guaranteed if the SRC modules operate stable in open loop mode with the source for the entire load range and all operating points. For each SRC module, a single loop current control can be employed with a crossover frequency lower than the shore based current source crossover frequency. A simple PI controller or integrator can be used to implement the control as shown in Fig. 6. In Fig. 6, a 180° inversion is included in the feedback loop due to the negative gain of the SRC from phase input to current output, as seen in (15). The saturation block in

Saturation

-+

Phase shift modulation

Zo

Iout

PI/ Integrator

-+

Iref

180° Fig. 6. Controller architecture.

Fig. 6 is employed to limit the minimum phase shift due to the resulting high input voltage discussed in the steady state analysis. Each SRC module in the system is controlled by its own controller independently. C. Discussion For a cascaded system which contains output regulated power converters, the regulated converter presents a constant load to the source subsystem because all load is on the regulated side of the converter. For example, if the input current drops, the power converter compensates and the input voltage increases. This means that the source subsystem will see a negative load resistance, and the system may become unstable. In the design of RF integrated circuits (IC), a resistor in parallel with the input to the IC or in series with the output (as appropriate) is employed as a solution to avoid oscillation caused by the negative resistance [8]. The power loss associated with this technique is acceptable in RF work, but not in a power system. For a power system, especially for a constant voltage cascaded power system, the general approach is to design an input filter for the load power converter accordingly. However, for a dc constant current power distribution system, the approach applied in RF work may be acceptable as well because of the different structure it has. For the undersea constant current power distribution system investigated in this paper, the entire trunk cable generally has a length of tens of kilometers or even longer. The conventional underwater telecommunication cable is generally used as the trunk cable for its high quality, high reliability and relatively low cost. The underwater telecommunication cable has a typical resistance of around 1 Ω/km, which means that the total resistance of the trunk cable in an undersea constant current power distribution system is several hundred ohms. Since the regulated power converters are distributed along the trunk cable, the trunk cable resistance is in series with the input impedance of those power converters. In other words, the load impedance seen by the source subsystem is the sum of the negative resistances from the regulated power converters and the positive resistance from the trunk cable. Since the trunk cable resistance is unavoidable in such a scenario, the trunk cable is able to assist the system to be stable and avoid oscillation. The control strategy presented in this paper is robust against cable faults and converter faults as well. When the trunk cable is broken at any point, the trunk cable current

shunts to sea water, the output voltage of the shore based current source on the land will automatically vary so that the voltage at the fault point becomes ground voltage and the current from the source to the fault point remains constant. The SRC modules in the series chain are controlled independently, so the energized modules can still operate as normal. The fault point can also be located by measuring the dc resistance between the source output and the ocean. When there is a converter fault in the system, such as the SRC module’s output open circuit fault, the controller will short the input of that module to bypass the trunk current to the rest of the system. The shore based current source on the land will automatically maintain the trunk current to be constant, and the rest of the system can operate without disturbances. In addition, shorting the input of an SRC module will reduce the total input impedance of the load subsystem while the output impedance of the source subsystem remains the same, so the whole system will be still stable as analyzed in section A.

Fig. 7. Reference step down transition. From top to bottom are output current, output voltage and input voltage of the SRC module.

IV. EXPERIMENTAL VALIDATION A. Single SRC Module Operation As the first step, experiments are conducted in order to validate that the SRC module is stable individually. The SRC module is a 100 kHz, 500 W SRC with 1:1 transformer turns ratio, 200 μH resonant inductor, 34 nF resonant capacitor, 1 A input current and regulated output current. An integral type controller is employed to control the output current of the SRC, as illustrated in Fig. 6. The controller has been designed to have a bandwidth of 10 Hz, and digitally implemented using a Xilinx VIRTEX 5 FPGA. Figure 7 shows the waveforms for the reference step down from 0.33 A to 0.2 A, where the blue trace (CH1) is the output current of the SRC module, the pink trace (CH3) is the input voltage and the green trace (CH4) is the output voltage. The load resistance used in this experiment is 1 kΩ.

Fig. 8. Load step up transition. From top to bottom are output current, output voltage and input voltage of the SRC module.

Figure 8 illustrates the hardware results for the load resistance step up from 700 Ω to 1 kΩ, where the blue trace (CH1) is the output current of the SRC module, the pink trace (CH3) is the input voltage and the green trace (CH4) is the output voltage. The output current reference used in this test is 0.33 A. From Fig. 7 and Fig. 8, the hardware results validate that the SRC module is stable individually by using the controller which has a crossover frequency lower than the source controller bandwidth. B. System Operation The scenario investigated in this paper is constant current dc distribution in undersea applications with a single shorebased source and multiple loads distributed along the cable, as illustrated in Fig. 1. The hardware experiments are conducted to validate the proposed control approach on a system consisting of two 500 W SRC modules connected in series and fed with 1 A constant input current. The parameters of the SRC modules and details of the controller are listed in the above section.

Fig. 9. Reference step up transients on SRC #1. From top to bottom are output current of SRC #1, input voltage of SRC #1, output current of SRC #2, and input voltage of SRC #2.

The experimental results are shown in Figs. 9-12, where the blue trace (CH1) is output current of SRC #1, the light blue trace (CH2) is input voltage of SRC #1, the pink trace (CH3) is output current of SRC #2 and the green trace (CH4) is input voltage of SRC #2. First, the system response for output current reference step change on SRC #1 is demonstrated. Fig. 9 shows the results for current reference of SRC #1 stepped up from 0.2 A to 0.33 A, while Fig. 10 shows the system response for current reference

shows the experimental results for SRC #1’s load resistance stepped down from 1 kΩ to 700 Ω. The load resistance for SRC #2 is 1 kΩ during this test. The output current reference of SRC #1 is set to be 0.33 A, and the output current reference of SRC #2 is set to be 0.2 A, for the same reason mentioned earlier .

Fig. 10. Reference step down transients on SRC #1. From top to bottom are output current of SRC #1, input voltage of SRC #1, output current of SRC #2, and input voltage of SRC #2.

Fig. 11. Load step up transients on SRC #1. From top to bottom are output current of SRC #1, input voltage of SRC #1, output current of SRC #2, and input voltage of SRC #2.

From Fig. 9-12, it can be seen that the transient on SRC #1 introduces a small disturbance on SRC #2, which is expected since the current source is not ideal. The hardware results validated the control strategy proposed in this paper, which is that the SRC modules are controlled independently with no communications required among them, by having a controller crossover frequency lower than the source controller bandwidth. V. CONCLUSION The constant current dc DPS is preferred for some applications in which power converter modules are connected in series and have a constant current input. This paper proposes a control strategy for series connected SRC modules in constant current dc DPS. The steady state solution of SRC with constant current input is presented, which is different from constant voltage input case. Stable operation of the system and independent regulation of the SRC output current is achieved through a low crossover frequency controller with no communications required among modules. Experimental results demonstrated stable operation of the system and regulation of the SRC modules’ output currents. The control strategy proposed in this paper works for the output voltage regulation scenario, the terrestrial constant current dc DPS and the constant voltage dc DPS as well, even though it is demonstrated for an undersea constant current dc DPS application with SRC’s output current regulated.

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[4] Fig. 12. Load step down transients on SRC #1. From top to bottom are output current of SRC #1, input voltage of SRC #1, output current of SRC #2, and input voltage of SRC #2.

of SRC #1 stepped down from 0.33 A to 0.2 A. The load resistance for both SRC modules is 1 kΩ during this experiment. The output current reference of SRC #2 is set to be 0.2 A in order to show the capability of regulating the output current to different values for different modules. Then, the experimental results for load step change on SRC #1 are shown. Fig. 11 shows the system response for SRC #1’s load resistance stepped up from 700 Ω to 1 kΩ, while Fig. 12

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